Question
the hot air balloon rises from 50 feet above the ground to 200 feet above the ground in 7 minutes what is the rate of change in the balloons altitude
Answers
GPT-4o mini
To find the rate of change in the balloon's altitude, you can use the formula for the rate of change, which is:
\[
\text{Rate of Change} = \frac{\text{Change in altitude}}{\text{Time taken}}
\]
1. **Change in altitude**: The balloon rises from 50 feet to 200 feet.
\[
\text{Change in altitude} = 200 \, \text{feet} - 50 \, \text{feet} = 150 \, \text{feet}
\]
2. **Time taken**: The rise occurs over 7 minutes.
3. **Calculating the rate**:
\[
\text{Rate of Change} = \frac{150 \, \text{feet}}{7 \, \text{minutes}} \approx 21.43 \, \text{feet per minute}
\]
Therefore, the rate of change in the balloon's altitude is approximately **21.43 feet per minute**.
\[
\text{Rate of Change} = \frac{\text{Change in altitude}}{\text{Time taken}}
\]
1. **Change in altitude**: The balloon rises from 50 feet to 200 feet.
\[
\text{Change in altitude} = 200 \, \text{feet} - 50 \, \text{feet} = 150 \, \text{feet}
\]
2. **Time taken**: The rise occurs over 7 minutes.
3. **Calculating the rate**:
\[
\text{Rate of Change} = \frac{150 \, \text{feet}}{7 \, \text{minutes}} \approx 21.43 \, \text{feet per minute}
\]
Therefore, the rate of change in the balloon's altitude is approximately **21.43 feet per minute**.